Embedded health monitoring system based upon Optimized Neuro Genetic Fast Estimator (ONGFE)

ABSTRACT

A real time kernel for deploying health monitoring functions in Condition Base Maintenance (CBM) and Real Time Monitoring (RTM) systems is disclosed in this invention. The Optimized Neuro Genetic Fast Estimator (ONGFE) allows embedding failure detection, identification, and prognostics (FDI&amp;P) capability by using Intelligent Software Element (ISE) based upon Artificial Neural Network (ANN). ONGFE enables embedded fast and on-line training for designing ANNs, which perform very high performance FDI&amp;P functions. An advantage is the optimization block based on pseudogenetic algorithms, which compensate for effects due to initial weight values and local minimums without the computational burden of genetic algorithms. It provides a synchronization block for communication with secondary diagnostic modules. Also a scheme for conducting sensor data validation is embedded in Smart Sensors (SS). The algorithms are designed for a distributed, scalar, and modular deployment. The system electronics is built upon a network of smart sensors and a health monitoring computer for providing data acquisition capability and distributed computational power.

CROSS REFERENCE OF RELATED APPLICATION

This is a regular application of a provisional application having anapplication No. 61/335,355 and a filing date of Jan. 5, 2010.

BACKGROUND OF THE INVENTION

1. Field of Invention

The present invention relates to a method for designinghealth-monitoring systems based upon an optimized embedded kernel forperforming FDI&P in CBM and RTM systems. In this invention the EmbeddedOptimized Neuro Genetic Fast Estimator (ONGFE) instantiates ISEs, whichare tailored for conducting FDI&P. Each ISE monitors a system componentstatus. Then health monitoring at the system level is performed bylinking ISEs. Distinctive characteristics of the embedded kernel andcomputational hardware platform are: fast learning; ANN optimization bynovel pseudogenetic algorithm; on-line learning; methods forsynchronization and communication with secondary diagnostic modules;highly distributed software and hardware architecture; real timeoperation; and embedded sensor data validation algorithm.

2. Description of Related Arts

Health monitoring (HM) refers to a set of techniques (algorithms) andtheir implementation, which are used for tracking system operationalcondition. They aim to achieve high reliability, availability, safety,and maintainability by conducting failure detection and prognostics.Based on this kind of technology maintenance practices, real timemonitoring, and depot operation can be enhanced and automated forreducing cost, keeping critical assets in operation, avoidingcatastrophic failures, supporting efficient maintenance practices, andmanaging resources. A particular example is its use for implementationof CBM systems where scheduled maintenance practices are replaced byschemes where maintenance is driven based on the system operationalcondition instead. Many applications can be listed for exemplifying thetechnological impact of health monitoring systems. Examples include(among many others) CBM and RTM for: aircraft's engines, ships'turbines, airplane structures, actuators, and on ground vehicles'systems. In the last years, great effort has been conducted by differentgovernment agencies promoting research and development in HM, CBM, andRTM. For example, NASA has been strongly supporting the development ofnovel innovative technologies to detect failures in propulsion systems(engines), exploration platforms, and in different aerospace vehicles.By achieving efficient health monitoring capability then reliable CBMand RTM can be provided.

SUMMARY OF THE PRESENT INVENTION

It is an objective of this invention to provide ISE, which definesoperands (data structures) that can be used with operators (instantiatedthrough algorithm implementation) for building health-monitoringfunctions. Within the scope of this invention an operand corresponds toANN data (weights, thresholds, number of inputs, hidden units, andnumber of outputs) and operators correspond to algorithms that processANN data (examples are learning algorithms, network pruning, fuzzyoperators, and network optimization). In this way ISE are arguments tooperators for creating a new ISE. The ISEs not only are arguments toONGFE's operators but also can be processed by new additional algorithmswhen implementing the health monitoring system.

Another objective of the present invention is to provide a method forembedding different types of health monitoring functions based on ISEfor constructing a diversity of real time health monitoring systems. Theresulting ISE provides a mechanism for performing failure: (a)Detection; (b) Identification; and (c) Prognostics. Capabilities (a) and(b) can be carried out individually (i.e. a single ISE per function) orboth capabilities can be combined in a single ISE. Prognostics will beconducted by a different ISE. Linking ISEs a full set of healthmonitoring capabilities can be customized for monitoring components,subsystems, and systems.

Another objective of the present invention is to provide very flexiblesystem architecture with the required granularity for inspecting eachpart that conform to the target system. A scheme that builds on ISEs,distributed hardware, and distributed health monitoring software kernelprovides a framework that can be adapted with the required level ofdetail for extracting system information and deploying diagnosticalgorithms in a distributed way.

Another objective of this invention is to provide a method forperforming real time failure detection and identification (FDI) insensor clusters. The ONGFE provides a method for sensor data estimationby processing data from sensor clusters. Sensor cluster data for a givenoperation range is used for designing an ISE estimator for predictingsensor outputs. Predicted sensor signals can be used for performingresidual analysis and determining sensor health.

Another objective of this invention is to provide a method forperforming real time FDI in systems and subsystems. The ONGFE provides amethod for deploying intelligent elements in computerized anddistributed hardware platform based on trained ANN for on-line and realtime FDI. These intelligent elements process in real time input featuresextracted from raw sensor data.

Another objective of this invention is to provide on-line fast learningto allow the ISE to learn to recognize system failures when performingon-line processing. For achieving real time operation in healthmonitoring systems, a detailed design considering time constraintsshould be achieved. Then approaching learning by embedding fastalgorithms is a required design constraint, which is embedded in thisinvention.

Another objective of this invention is to provide a scalable HMK withmethods (communication and synchronization) for compiling differentdiagnostic techniques that can work in a collaborative way. A healthmonitoring processing framework with communication and synchronizationmechanisms for interacting with other learning paradigms and diagnostictools enables (building upon the ONGFE's HMK) compiling diversetechniques within a common framework. In this way, several learningschemes can coexist within a single learning engine.

Another objective of this invention is to provide a scheme for embeddingevolving diagnostic capability. This is achieved by: (a) dynamical HMK(which performs ISE instantiation and customization by application ofon-line operations); (b) communication and synchronization mechanism;(c) on-line learning; and (d) application program interface (API). Inthis way mechanisms for discovering new behaviors can be synchronizedwith the ONGFE's HMK for evolving the ISE's diagnostic capabilities.External conditions can trigger learning for recognizing new healthstates and adding dynamically new health knowledge (learn-to-learncapability).

Another objective of this invention is to provide ISE with capability toperform failure prognostics. A regression method for time estimation offailure occurrence is provided by ONGFE's ANN designed by usinghistorical data. By applying high performance learning for embeddingfunction approximation capability the resulting ISE performs as a timefailure estimator in the prognostic framework.

Another objective of this invention is to provide an optimizationprocess for enhancing ISE's prognostic capability. A population of ANN(each one designed as time failure estimator) is the input to apseudogenetic algorithm for performing ANN optimization.

Another objective of this invention is to provide a real timedistributed, scalar, and modular computational hardware platform forproviding a flexible system structure that can be tailored to a widerange of applications.

Additional advantages and features of the invention will become apparentfrom the description which follows, and may be realized by means of theinstrumentalities and combinations particular point out in the appendedclaims.

According to the present invention, the foregoing and other objects andadvantages are attained by a system of health monitoring computer (HMC),adapted for communicating with a target system through a sensor networkand collecting health data from the target system, and for interactivelycommunicating with secondary diagnostic modules for the target system,comprising:

an Embedded Health Monitoring based upon Optimized Neuro Genetic FastEstimator (ONGFE), comprising a communication and synchronization blockinteractively communicating with the secondary diagnostic modules forthe target system;

a Health Monitoring Inference Mechanism (HMIM) communicating with theOptimized Neuro Genetic Fast Estimator (ONGFE), having a plurality ofIntelligent Software Elements ISEs which are designed and embedded inthe Health Monitoring Inference Mechanism (HMIM) through the OptimizedNeuro Genetic Fast Estimator (ONGFE),

wherein the Health Monitoring Inference Mechanism (HMIM) is arranged foroperatively communicating with the sensor network embedded with ISEsdesigned by the Optimized Neuro Genetic Fast Estimator (ONGFE),

wherein the sensor network is arranged for extracting physicalparameters measurements from the target system and generating andinputting the health data including sensor data, status and features tothe Health Monitoring Inference Mechanism (HMIM) and Embedded HealthMonitoring based upon Optimized Neuro Genetic Fast Estimator (ONGFE),

wherein the sensor network comprises a plurality of smart sensors whichare customizable according to the target system, wherein a baselinesensor suit of the sensor network is formed with temperature, flow,pressure, and vibration sensors,

wherein each of the smart sensors having low power consumption iscapable of providing data acquisition, sensor data validation, a libraryof feature extraction algorithms and communication capabilities,

wherein each of the smart sensors comprises a sensor data validationcore for signal processing; and

a communication block communicating with the Health Monitoring InferenceMechanism (HMIM), wherein the Health Monitoring Inference Mechanism(HMIM) generates health assessments in response to the health data fromthe sensor network and provides the health assessments to thecommunication block for feeding Man Machine Interfaces of the targetsystem;

thereby each of the Intelligent Software Elements ISEs, which aredesigned through the Optimized Neuro Genetic Fast Estimator (ONGFE)which interactively communicates with the secondary diagnostic modulesfor the target system and the sensor network, is capable of performingone function when the function is prognostic function, and is capable ofperforming one or more function when the function includes failuredetection function and failure identification function.

In accordance with another aspect of the invention, the presentinvention is a method for conducting data validation in cluster ofsensors (correlated sensors) embedded in a smart sensor, which isadapted for communicating with a system of health monitoring computer(HMC) having a Optimized Neuro Genetic Fast Estimator ONGFE, comprisingthe steps of

(a) performing design of sensor signals estimator ISE 631 by usingfunction estimation learning capability of the ONGFE;

(b) performing on-line sensor signals estimation by using the ISE 631 ofsaid ONGFE which has embedded function estimation capability;

(c) generating a residual value vector; and

(d) feeding the residual value to said ISE 631 of said ONGFE which hasembedded FDI capability 635 for performing sensor health assessment.

Still further objects and advantages will become apparent from aconsideration of the ensuing description and drawings.

These and other objectives, features, and advantages of the presentinvention will become apparent from the following detailed description,the accompanying drawings, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating the components of the Embedded HealthMonitoring System based upon Optimized Neuro Genetic Fast Estimator(ONGFE).

FIG. 2 is a diagram illustrating the components of the Embedded HealthMonitoring System based upon Optimized Neuro Genetic Fast Estimator(ONGFE) with the Smart Sensors building blocks, which consist ofintegrated sensors, data acquisition, data validation algorithms,feature extraction, and Smart Sensor Communication block.

FIG. 3 is a diagram illustrating the components of the Embedded HealthMonitoring System based upon Optimized Neuro Genetic Fast Estimator(ONGFE) with the Inference Health Monitoring Mechanism (IHMM) for FDI&Pand optimization block.

FIG. 4 is a diagram illustrating the sensor data validation scheme forcorrelated signals in sensor clusters.

FIG. 5 is a diagram illustrating the Multilayer Perceptron (MLP) that isused for building the Intelligent Software Elements.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

An ensemble of technologies is required for embedding HM capability.Involved technologies include: (a) embedded smart sensors; (b) dataprocessing methods that focus on extracting features or conditionindicators from raw data; (c) sensor fusion tools; (d) sensor datavalidation algorithms; (e) suitable networking software and hardware(vehicle/automotive sensor networks, aircraft data networks, wireless,and LAN communications); (f) real time operating systems; (g) ManMachine Interface (MMI); (h) automated identification technology; (i)enhanced diagnostics and prognostics; and (j) failure trend analysis.Enhancements to the process include data mining (for discovering to newbehaviors but also correlations between features (symptoms) andfailures) and integration to information systems (configurationmanagement, depot databases, maintenance management automation, andinternet servers) to implement CBM-plus type systems.

Key elements in the HM processing framework are (a) enhanced diagnosticsand (b) prognostics, which are crucial steps when providing healthassessments. The main processing flow consists of sensors collectingcomponent/system data, validation of sensor data, data aggregation,feature extraction, diagnostics, and prognostics for providing healthassessments in a MMI.

Referring to FIG. 1 of the drawings, the ONGFE is a computerizeddistributed health monitoring kernel (HMK) specifically designed forhigh performance diagnostics and enhanced prognostics. In the ONGFEkernel, both diagnostics and prognostics are conducted by embeddedArtificial Neural Network (ANN) designed on-line with fast learning forachieving real time operation. The prognostic capability is optimized byusing a pseudogenetic algorithm in order to embed evolving capabilitybut avoiding a heavy computational load. The system architecture isdesigned in a distributed way in order to obtain a scalable, modular,and flexible health monitoring system, as shown at FIG. 1.

A flexible HMK that can automatically learn to recognize system failureswhen the system is in operation is required. On-line fast diagnosticlearning and synchronization methods enable recognizing new failures(i.e. self-adaptability capability) for dynamically tailoring the healthmonitoring capabilities during the system operation. A scalable modularHMK with communication and synchronization methods for compilingdifferent techniques that can work in a collaborative way is alsorequired for enhancing the health monitoring capabilities. Consideringsensor data accuracy the ONGFE provides an embedded method forperforming sensor data validation. Prognostics of critical failures is achallenging problem and has been approached in several ways. Techniquesinclude Bayesian networks, Kalman Filters, advanced statistical models,among others. But still, needed is a highly reliable solution in orderto integrate accurate prognostics. The ONGFE's ANNs provide an optimizedregression method for enhanced prognostics. A two-step process isinvolved: (1) prognostic estimator design is conducted based on ANN andhistorical data and (2) optimization of the resulting estimators isapproached by an innovative pseudogenetic algorithm. Thus, a highlydistributed scalable real-time hardware with HMK for high performanceand reliable FDI&P is a need for development of robust CBM and RTMsystems.

The present invention is based on advanced distributed real time dataacquisition, preprocessing algorithms, embedded systems, artificialintelligence, and electronic technologies. As shown at FIG. 1 the ONGFE40, Health Monitoring Inference Mechanism (HMIM) 30, communication block20, and Sensor Communication Block (SCB) 50 are embedded in a HealthMonitoring Computer (HMC) 10. Smart Sensor (SS) 60 provides transducers(sensor), data acquisition capability, processing capability, sensordata validation, feature extraction algorithms, data log capability, andhardware communications for implementing a real time distributed dataacquisition sensor network. Different types of sensors can be attachedto the SS 60 for monitoring physical variables of the system (such asvibration, temperature, pressure, flow, etc.). FIG. 1 shows the HMC 10and a single SS 60. The number of SS 60s that conform to the wirelessnetwork is a function of the data acquisition requirements. According tothis, then the number of SS 60 is defined, and wireless communication(Zigbee standard) is used for creating a wireless network. Each SS 60handle up to 8 transducers (sensors) and the maximum sampling period is200 k samples. Sensor data is collected in the HMC 10. Healthinformation consisting of measurements from sensors, snapshots, andhealth assessments are fed to customized MMI. For doing this, the HMC 10provides a communication block 20 for transferring health informationthrough a communication channel (Ethernet, I²C, RS232, and IEEE 802.11that are embedded in the HMC's communication block 20). In addition tothis, the HMC 10 has a Sensor Communication Block 50 (Zigbee, IEEE802.15.4, I²C, RS-232, and USB are core interfacing mechanisms), whichinterfaces with the Zigbee coordinator for extracting data from the towireless network of Smart Sensors. This interface receives sensor dataand features from a wireless networks or smart sensors and feeds theHMIM 30 and the ONGFE 40. The HMIM 30 delivers health informationconsisting of health assessments, measurements, snapshots of sensordata, and row data to the communication block 20 which transfers thisinformation to external devices. The communication block 20 provides asecond networking level (in addition to the sensor network level), whichallows interconnecting with several HMC 10 to central devices providinga very flexible system structure for deploying hardware and healthmonitoring algorithms. This system structure is suitable forimplementing a system of systems in a scalar, modular, and distributedarchitecture.

Each SS 60 complies to the requirements for ultra low power consumption(with a supply Voltage Range of 1.8 to 3.6 v and 0.7 microamperes inStandby Mode and 200 microamperes at 1 MHZ with 2.2 volts), providedifferent acquisition modes (single input single sample; sequence ofchannels single sequence; single input and multiple samples; sequence ofchannels and multiple sequences), programmable sample period, andretention times. Considering fast sensors (accelerometers for vibrationmonitoring) sampling periods up to 200 k samples are provided. In FIG. 2shows the building blocks of the SS 60. Sensors 61 (transducers) provideelectrical signals from physical parameters (vibration, flow, pressure,etc.) of the system 70. The sensor 61 provides voltages and currents tothe Data Acquisition 62 system, which converts the analog signal intodigital data according to the defined sampling period and retentiontime. After digitizing the signals, the data is processed by the DataValidation block 63. A method for performing sensor data validation inthe case of clusters of correlated sensor is embedded within the DataValidation block 63. FIG. 4 shows the structure of this scheme. Thenvalidated data is delivered to the Feature Extraction block 64. For slowsensor (such as temperature and flow) features, that are extracted,consist of rms value, low pass filter of the signal, and firststatistics moments. In the case of vibration additional extractedfeatures are crest factor, kurtosis, and main vibration frequencies.Customized algorithms can be embedded. Finally, snapshots of sensor rawdata and features are transferred through the Smart Sensor CommunicationBlock (SSCB) 65 to the HMC 10. The SSCB 65 provides different types ofcommunication channels, which include; I²C, RS232, SPI, IEEE 802.15.4,and Zigbee.

There are three main operation modes in the HMC 10. The first one is anormal operation mode, where sensor features and sensor data areprocessed by ISEs based upon trained ANN (shown at FIG. 5), whichconducts FDI&P in the HMIM 30. The second operation mode deals withsetting up the system by training and optimization. Fast training 41 isperformed to every ISE, both for performing FDI by doing patternrecognition (ISE 31, ISE 32 and ISE 33 in FIG. 3 and ISE 635 in FIG. 4)and the ones that perform function estimation for doing prognostics (ISE34 in FIG. 3) and sensor data estimation (ISE 631 in FIG. 4). In thecase of prognostics an additional step is optimization by pseudogeneticblock 43. The third operation mode refers to working in a collaborativeway with external diagnostic schemes. A synchronization block 44 is thecomponent that provides methods for interacting with other secondarydiagnostic modules (SDM) 80. Interaction capability with SDM 80 combinedwith on-line real time fast learning schemes 41 enable embeddingevolving capability in the Embedded Health Monitoring System based uponONGFE. Adding knowledge for new failures recognition is achieved byconducting learning in an event trigger base. For example, events can begenerated by: (a) the SDM 80 and (b) when the sensor signals or featurestake a value above a defined red line and the condition does notcorrespond to a known failure. Once an event is detected then samples ofsensor data and corresponding features are used for modifying theintelligent elements in order that they can recognize this new workingcondition (failure) by retraining the corresponding ISE. In this way, bycombining these three operation modes the system can recognizecharacterized failures as well as learn new unknown conditions bytriggering learning.

In the HMIM each, low level (in the two level structure shown at FIG. 3)ISE is coupled with a component or subsystem. The case of two componentsand their corresponding ISE is shown at FIG. 3. ISE 31 performs FDI fora first component, and ISE 32 performs FDI for a second component.System monitoring and customization is achieved by linking severalintelligent elements. FIG. 3 demonstrates this with ISE 31 and ISE 32,which feeds ISE 33 for performing FDI at the system level. When afailure is recognized by either ISE 31 or ISE 32, then a failureidentifier is sent to the ISE 33, which also processes features andsensor data for performing FDI at the system level (failurepropagation). These elements (ISE 31, ISE 32, and ISE 33) consist ofalready trained ANN (from operation mode two or three) that processes inreal time features and sensor data at the component level and systemlevel. The structure of the ISE is shown at FIG. 5. According to thefigure then each ISE consists of a Multilayer Perceptron (MLP). Thenumber of inputs (N) in the MLP is defined by the number of features andsamples of sensor signals. The number of outputs of the MLP it isdefined by the number of failures (equal to M−1) to be recognized and anadditional output for indication of normal operation. On the other handconsidering a time failure estimator, a single output provides thefailure prognostic time (M=1). From FIG. 5, the net value and the outputvalue for the j^(th)-hidden unit for the p^(th) training pattern aredefined as

${net}_{p,j} = {\sum\limits_{i = 1}^{N + 1}{{w\left( {j,i} \right)} \cdot x_{p,i}}}$1 ≤ p ≤ N_(v), 1 ≤ j ≤ N_(h) _(p, j) = f(net_(p, j))

Here the threshold of the j^(th) node is handled by defining x_(p,N+1)as one. Weight w(j,i) connects the i^(th) input to the j^(th) hiddenunit. The activation function ƒ is the sigmoid function in the units ofthe hidden layers and linear functions for the units in the outputlayer. In a two layer MLP the j^(th) output in the hidden layer is givenby,

$O_{p,j} = {{f\left( {net}_{p,j} \right)} = {\frac{1}{1 + {\mathbb{e}}^{- {net}_{p,j}}}.}}$

The k^(th) output for the p^(th) training pattern is given by,

$y_{p,k} = {{\sum\limits_{i = 1}^{N + 1}{{w_{o}\left( {k,i} \right)} \cdot x_{p,i}}} + {\sum\limits_{j = 1}^{N_{k}}{{w_{o}\left( {k,{j + N + 1}} \right)} \cdot O_{p,j}}}}$1 ≤ k ≤ M

The mapping error for the p^(th) pattern is

${E_{p} = {\sum\limits_{k = 1}^{M}\left\lbrack {t_{p,k} - y_{p,k}} \right\rbrack^{2}}},$

where t_(p,k) denotes the k^(th) element of the p^(th) desired outputvector. In order to train a neural network, for one epoch, the mappingerror for the k^(th) output unit is defined as

${E(k)} = {\frac{1}{N_{v}}{\sum\limits_{p = 1}^{N_{v}}{\left\lbrack {t_{p,k} - y_{p,k}} \right\rbrack^{2}.}}}$

where N_(v) is the number of patterns (examples) that form the trainingdata file. The overall performance of a MLP network, measured as MeanSquare Error (MSE), can be written as

$E = {{\sum\limits_{k}^{M}{E(k)}} = {\frac{1}{N_{v}}{\sum\limits_{p = 1}^{N_{v}}{E_{p}.}}}}$

Training is conducted by using the OWO-HWO algorithm embedded in theONGFE's 40 Fast Training Kernell 41, which performs output weightoptimization (OWO) in the output layer for finding the weights. Then,the HWO step uses separate error functions for each hidden unit andfinds the optimal weights connecting to the hidden units. However, thisrequires desired hidden net functions, which are not normally available.They can be estimated asnet_(pd,j)≅net_(p,j) +Z·δ _(p)(j),

where net_(pd,j) is the desired net function and net_(p,j) the actualnet function for the j^(th) unit and the p^(th) pattern. Z is thelearning factor and δ_(p)(j) is the gradient of the j^(th) hidden unitactivation with respect to its net function.

The error function is given by,

${{E_{\delta}(j)} = {\frac{1}{N_{v\;}}{\sum\limits_{p = 1}^{Nv}\left\lbrack {{\delta_{p}(j)} - {\sum\limits_{i = 1}^{N + 1}{e_{ji} \cdot x_{p,i}}}} \right\rbrack^{2}}}},$

where e_(ji) is obtained solving the following set of equations in theleast square sense

${\delta_{p}(j)} \cong {\sum\limits_{i = 1}^{N + 1}{e_{ji} \cdot {x_{p,i}.}}}$

In OWO-HWO the hidden weights will be updated byw(j,i)=w(j,i)+Δw(j,i)=w(j,i)+Z·e _(ji).

In one iteration, the total change in the error function E, due tochanges in all hidden weights, can be approximated as

${\Delta\; E} \cong {{- Z}\frac{1}{N_{v}}{\sum\limits_{j = 1}^{Nh}{\sum\limits_{p = 1}^{Nv}{{\delta_{p}^{2}(j)}.}}}}$

In some cases, the approximation of (last equation) may be invalid. Thealgorithm checks the convergence in the calculations and if it isnecessary it fixes the process when the error increases by restoringprevious results and reducing Z.

Prognostics are triggered when a degradation of the sensor readings orfeature is recognized. Working with nominal operating points, theexpected values of sensor data correlated with system failures areknown. For a known operation point with stable conditions selectedsensor readings and features are monitored, and trend analysis isperform for detecting degradation in their values. Prognostic isconducted when the starting of a trend is identified, which is conductedby performing function approximation by using an MLP. Statistical datais used for defining the training data file for doing functionestimation. At FIG. 3, ISE 34 conducts prognostics by performingfunction estimation. Then ISE 34 provides an estimate of the remaininguseful life of the component or system. Optimization of the prognosticprocess in the ISE 34 is performed by the ONGFE 40. As shown at FIG. 3,the algorithm works with a Population of MLPs (P-ISE) 42. Thispopulation is processed by a Pseudogenetic (PG) block 43. The embeddedalgorithm is based on a modified version of the Schmidt procedure (withthe purpose of reducing execution time within the pseudogeneticalgorithm). This form of the Schmidt process makes it possible to obtainexpressions for the output error of the network as a function of thenumber of units being pruned. Here the m^(th) orthonormal basis functionx_(m)′, can be expressed as

$\begin{matrix}{x_{m}^{\prime} = {\sum\limits_{k = 1}^{m}{a_{mk}{x_{k}.}}}} & (1)\end{matrix}$

From equations (1) with m=1, the first basis function is obtained as

$\begin{matrix}{{x_{1}^{\prime} = {{\sum\limits_{k = 1}^{1}{a_{1k}x_{k}}} = {a_{11}x_{1}}}},{a_{11} = {\frac{1}{x_{1}} = \frac{1}{{r\left( {1,1} \right)}^{1/2}}}},} & (2)\end{matrix}$

where r(1,1) is the first element of the autocorrelation matrix and

${r\left( {i,j} \right)} = {{E\left\lbrack {x_{i} \cdot x_{j}} \right\rbrack} = {\frac{1}{Nv}{\sum\limits_{p = 1}^{Nv}{x_{p,i} \cdot x_{p,j}}}}}$

From equation (1) with m=2, the second basis function is

$\begin{matrix}{{x_{2}^{\prime} = {{\sum\limits_{k = 1}^{2}{a_{2k}x_{k}}} = {{a_{21}x_{1}} + {a_{22}x_{2}}}}},} & (3)\end{matrix}$

but also

$\begin{matrix}{\begin{matrix}{x_{2}^{\prime} = \left. \frac{z_{2}}{z_{2}}\Rightarrow \right.} \\{z_{2} = {{x_{2} - {c_{1}x_{1}^{\prime}}} = {x_{2} - {c_{1}a_{11}x_{1}}}}}\end{matrix}{\left( {{{with}\mspace{14mu} c_{1}} = \left\langle {x_{1}^{\prime},x_{2}} \right\rangle} \right),}} & (4)\end{matrix}$

we can say,

$\begin{matrix}{{z_{2} = {{\sum\limits_{k = 1}^{2}{b_{k}x_{k}}} = {{b_{1}x_{1}} + {b_{2}x_{2}}}}},} & (5)\end{matrix}$

where from (4) and (5),b ₁ =−c ₁ a ₁₁b ₂=1.

Defining “g” as the denominator of x₂′ then,

$\begin{matrix}\begin{matrix}{g^{2} = \left\langle {{x_{2} - {c_{1}x_{1}^{\prime}}},{x_{2} - {c_{1}x_{1}^{\prime}}}} \right\rangle} \\{{= {{r\left( {2,2} \right)} - c_{1}^{2}}},}\end{matrix} & (6)\end{matrix}$

so that from equations (3), (5) and (6),

$\begin{matrix}{{{x_{2}^{\prime} = {{{a_{21}x_{1}} + {a_{22}x_{2}}} = \frac{{b_{1}x_{1}} + {b_{2}x_{2}}}{g}}},{a_{21} = {\frac{b_{1}}{g} = \frac{{- c_{1}}a_{11}}{\left( {{r\left( {2,2} \right)} - c_{1}^{2}} \right)^{1/2}}}}}{{a_{22} = {\frac{b_{2}}{g} = \frac{1}{\left( {{r\left( {2,2} \right)} - c_{1}^{2}} \right)^{1/2}}}},{with}}{c_{1} = {\left\langle {x_{1}^{\prime},x_{2}} \right\rangle = {{E\left\lbrack {x_{1}^{\prime} \cdot x_{2}} \right\rbrack} = {a_{11}{r\left( {1,2} \right)}}}}}{a_{11} = {\frac{1}{x_{1}}.}}} & (7)\end{matrix}$

For the third basis function (m=3),

$\begin{matrix}{{{x_{3}^{\prime} = {{\sum\limits_{k = 1}^{3}{a_{3k}x_{k}}} = {{a_{31}x_{1}} + {a_{32}x_{2}} + {a_{33}x_{3}}}}},{{but}\mspace{14mu}{also}}}\text{}{x_{3}^{\prime} = \left. \frac{z_{3}}{z_{3}}\Rightarrow\begin{matrix}{z_{3} = {{x_{3} - {c_{1}x_{1}^{\prime}} - {c_{2}c_{2}^{\prime}}} =}} \\{{= {{\left( {{{- c_{1}}a_{11}} - {c_{2}a_{21}}} \right)x_{1}} - {c_{2}a_{22}x_{2}} + x_{3}}},}\end{matrix} \right.}{with}\begin{matrix}{c_{1} = {\left\langle {x_{1}^{\prime},x_{3}} \right\rangle = {E\left\lbrack {a_{11}x_{1}x_{3}} \right\rbrack}}} \\{= {a_{11}{r\left( {1,3} \right)}}}\end{matrix}\begin{matrix}{c_{2} = {\left\langle {x_{2}^{\prime},x_{3}} \right\rangle = {{E\left\lbrack {\left( {{a_{21}x_{1}} + {a_{22}x_{2}}} \right)x_{3}} \right\rbrack} =}}} \\{= {{a_{21}{r\left( {1,3} \right)}} + {a_{22}{{r\left( {2,3} \right)}.}}}}\end{matrix}} & (8)\end{matrix}$

The numerator in (8) is now,

$\begin{matrix}{{z_{3} = {{\sum\limits_{k = 1}^{3}{b_{k}x_{k}}} = {{b_{1}x_{1}} + {b_{2}x_{2}} + {b_{3}x_{3}}}}},} & (9)\end{matrix}$

where from (8) and (9),b ₁ =−c ₁ a ₁₁ −c ₂ a ₂₁b ₂ =−c ₂ a ₂₂b ₃=1.

Generalizing,

$b_{k} = {- {\sum\limits_{n = k}^{m - 1}{c_{n}a_{nk}}}}$k = 1, 2, …  , m − 1 b_(m) = 1,

Defining “g” as the denominator of x₃′,

$\begin{matrix}{{g^{2} = \left\langle {{x_{3} - {c_{1}x_{1}^{\prime}} - {c_{2}x_{2}^{\prime}}},{x_{3} - {c_{1}x_{1}^{\prime}} - {c_{2}x_{2}^{\prime}}}} \right\rangle},\begin{matrix}{g = \left( {{E\left\lbrack x_{3}^{2} \right\rbrack} - c_{1}^{2} - c_{2}^{2}} \right)^{1/2}} \\{= {\left( {{r\left( {3,3} \right)} - c_{1}^{2} - c_{2}^{2}} \right)^{1/2}.}}\end{matrix}} & (10)\end{matrix}$

From equations (8), (9) and (10)

$\begin{matrix}{{{{{x_{3}^{\prime}a_{31}x_{1}} + {a_{32}x_{2}} + {a_{33}x_{3}}} = \frac{{b_{1}x_{1}} + {b_{2}x_{2}} + {b_{3}x_{3}}}{g}},{a_{31} = {\frac{b_{1}}{g} = \frac{{{- c_{1}}a_{11}} - {c_{2}a_{21}}}{\left( {{r\left( {3,3} \right)} - c_{1}^{2} - c_{2}^{2}} \right)^{1/2}}}}}{a_{32} = {\frac{b_{2}}{g} = \frac{{- c_{2}}a_{22}}{\left( {{r\left( {3,3} \right)} - c_{1}^{2} - c_{2}^{2}} \right)^{1/2}}}}{{a_{33} = {\frac{b_{3}}{g} = \frac{1}{\left( {{r\left( {3,3} \right)} - c_{1}^{2} - c_{2}^{2}} \right)^{1/2}}}},{with}}{c_{1} = {\left\langle {x_{1}^{\prime},x_{3}} \right\rangle = {a_{11}{r\left( {1,3} \right)}}}}{{c_{2} = {\left\langle {x_{2}^{\prime},x_{3}} \right\rangle = {{a_{12}{r\left( {1,3} \right)}} + {a_{22}{r\left( {2,3} \right)}}}}},}} & (11)\end{matrix}$

where a₁₁ is defined by (2) and a₂₁, a₂₂ are defined by (7)

From equation (11), the c_(j) factors can be obtained in the followingway. For getting the “i” basis function, there will be a number equal to“i−1” of c_(j) factors, which can be obtained using

$\begin{matrix}{c_{n} = {\sum\limits_{k = 1}^{n}{a_{nk}{r\left( {k,m} \right)}}}} & {with} & {1 \leq n \leq {m - 1}} \\\; & \; & {{m > 1},}\end{matrix}$

For the third basis function (m=3) there will be two c_(j) factors, c₁and c₂.

Now we have the coefficients a_(nk) for 1≦n≦m−1, 1≦k≦n where m=3. Theremaining orthogonal basis functions, described as in (1), are foundinductively as follows. First coefficients b_(k) are found as,

$\left\{ {\begin{matrix}{b_{k} = {- {\sum\limits_{n = k}^{m - 1}{c_{n}a_{nk}}}}} & {1 \leq k \leq {m - 1}} \\{b_{k} = 1} & {k = {m.}}\end{matrix}\quad} \right.$

Then a_(mn) is found for 1≦n≦m as

$a_{mn} = {\frac{b_{n}}{\left\lbrack {{r\left( {m,m} \right)} - {\sum\limits_{k = 1}^{m - 1}c_{k}^{2}}} \right\rbrack^{1/2}}.}$

Working with the orthogonalized system is possible to obtain the errorof the original network. From this derivation it is obtained expressionsthat let us predict the error of the NN for different sizes. Also, fromthis equations, estimation of the energy of the network can beaccomplished. We can express the error in the i^(th) output node as,

$\begin{matrix}\begin{matrix}{{{E(i)} = {E\left\lbrack {\left( {t_{i} - {\sum\limits_{k = 1}^{Nu}{{w_{o}^{\prime}\left( {i,k} \right)}x_{k}^{\prime}}}} \right)\left( {t_{i} - {\sum\limits_{m = 1}^{Nu}{{w_{o}^{\prime}\left( {i,m} \right)}x_{m}^{\prime}}}} \right)} \right\rbrack}},} \\{{= {{E\left\lbrack t_{i}^{2} \right\rbrack} - {2{\sum\limits_{k = 1}^{Nu}{{w_{o}^{\prime}\left( {i,k} \right)}{E\left\lbrack {x_{k}^{\prime}t_{i}} \right\rbrack}}}} + {\sum\limits_{k = 1}^{Nu}\left( {w_{o}^{\prime}\left( {i,k} \right)} \right)^{2}}}},}\end{matrix} & (12)\end{matrix}$

Applying least square estimation we can get thatw′ _(o)(i,m)=E[x′ _(m) t _(i)].  (13)

Now using equation (1) we get,

$\begin{matrix}{{{w_{o}^{\prime}\left( {i,m} \right)} = {{\sum\limits_{k = 1}^{m}{a_{mk}{E\left\lbrack {x_{k}t_{i}} \right\rbrack}}} = {\sum\limits_{k = 1}^{m}{a_{mk}{c\left( {i,k} \right)}}}}},} & (14)\end{matrix}$

where c(i,k) is the an element of the crosscorrelation matrix defined as

${c\left( {i,k} \right)} = {{E\left\lbrack {x_{k} \cdot t_{i}} \right\rbrack} = {\frac{1}{Nv}{\sum\limits_{p = 1}^{Nv}{x_{p,k}{t_{p,i}.}}}}}$

From equations (12) and (13), the MSE at the i^(th) node is

$\begin{matrix}{{E(i)} = {{E\left\lbrack t_{i}^{2} \right\rbrack} - {\sum\limits_{k = 1}^{Nu}{\left( {w_{o}^{\prime}\left( {i,k} \right)} \right)^{2}.}}}} & (15)\end{matrix}$

Equation (15) is an exact result. It can be used for prediction of theerror of the Neural Network. This can be done when eliminating uselessbasis functions X′ and with this equation, estimating the expected errorafter pruning the network. Also, working with these output weights theenergy handled in the basis functions can be obtained.

In this way, working with the orthogonal system the effect of each basisfunction over the error of the ANN can be estimated. For transformingthe weights in the original NN from the orthogonalized system,considering the previous results we can say that,

$y_{i} = {{\sum\limits_{k = 1}^{Nu}{{w_{o}\left( {i,k} \right)}x_{k}}} = {\sum\limits_{m = 1}^{Nu}{{w_{o}^{\prime}\left( {i,m} \right)}{x_{m}^{\prime}.}}}}$

Working with the right hand side equation, and using equation (1)

${{\sum\limits_{m = 1}^{Nu}{{w_{o}^{\prime}\left( {i,m} \right)}x_{m}^{\prime}}} = {\sum\limits_{m = 1}^{Nu}{{w_{o}^{\prime}\left( {i,m} \right)}{\sum\limits_{k = 1}^{m}{a_{mk}x_{k}}}}}},$

Changing the upper limit from “m” to “N_(u)” and rearranging the sums,

$y_{i} = {{\sum\limits_{k = 1}^{Nu}{{w_{o}\left( {i,k} \right)}x_{k}}} = {\sum\limits_{k = 1}^{Nu}{\left\lbrack {\sum\limits_{m = 1}^{Nu}{{w_{o}^{\prime}\left( {i,m} \right)}a_{mk}}} \right\rbrack{x_{k}.}}}}$

With a_(mk)=0 if k>m, equation (4.40) becomes

$\begin{matrix}{{{y_{i} = {{\sum\limits_{k = 1}^{Nu}{{w_{o}\left( {i,k} \right)}x_{k}}} = {\sum\limits_{k = 1}^{Nu}{\left\lbrack {\sum\limits_{m = 1}^{Nu}{{w_{o}^{\prime}\left( {i,m} \right)}a_{mk}}} \right\rbrack x_{k}}}}},{and}}{{w_{o}\left( {i,k} \right)} = {\sum\limits_{m = k}^{Nu}{{w_{o}^{\prime}\left( {i,m} \right)}{a_{mk}.}}}}} & (16)\end{matrix}$

Using equation (16) we get the weights in the original domain of thenetwork.

In the modified orthogonalization process defined from page 16 line 12to page 20 line 13, raw basis functions are processed into orthonormalbasis functions in natural order. In other words, the m^(th) orthonormalbasis function is formed from the m^(th) raw basis function. In thispart the process is generalized, so that arbitrary ordering is allowed.Let j(m) be an integer valued function that specifies the order in whichraw basis functions x_(k) are processed into orthonormal basis functionsx_(k)′. In other words, x_(m)′ is to be formed from x_(j(m)). Note that1≦m≦N_(u) and 1≦j(m)≦N_(u). Generalizing the process defined at page 16line 12 to page 20 line 13, the m^(th) orthonormal basis function isdescribed as

$\begin{matrix}{x_{m}^{\prime} = {\sum\limits_{k = 1}^{m}{a_{mk}{x_{j{(k)}}.}}}} & (17)\end{matrix}$

Given the function j(k), we find a₁₁ for the basis function x₁′ as

$a_{11} = {\frac{1}{x_{j{(1)}}} = {\frac{1}{{r\left( {{j(1)},{j(1)}} \right)}^{1/2}}.}}$

For the function x₂′, a₂₁ and a₂₂ are found as

${a_{21} = \frac{{- c_{1}} \cdot a_{11}}{g}},{a_{22} = \frac{1}{g}},{where}$c₁ = a₁₁r(j(1), j(2)), g = (r(j(2), j(2)) − c₁²)^(1/2),

For basis functions x_(m)′ for m=3, 4, . . . , N_(u) coefficients a_(mk)are found next.

Now, assume that we have coefficients a_(nk) for 1≦n≦m−1 and 1≦k≦n. Thec_(n) coefficients are found as

$c_{n} = {\sum\limits_{k = 1}^{n}{a_{nk}{r\left( {{j(k)},{j(m)}} \right)}}}$1 ≤ n ≤ m − 1,

The b_(k) coefficients are found as

${b_{k} = {- {\sum\limits_{n = k}^{m - 1}{c_{n}a_{nk}}}}},{b_{m} = 1},$

for 1≦k≦m−1. Finally new coefficients a_(mn) are found as

$a_{mn} = {{{\frac{b_{n}}{\left\lbrack {{r\left( {{j(m)}{j(m)}} \right)} - {\sum\limits_{k = 1}^{m - 1}c_{k}^{2}}} \right\rbrack^{1/2}}.{for}}\mspace{20mu} 1} \leq n \leq {m.}}$

Selection of hidden units is performed by estimation of the basisfunction effect over the error or the network. The basis functions areordered, and according to the desired size of the hidden layer then thefirst neurons are selected for conforming to the hidden layer of thenetwork. The goal in this subsection is to get the function j(m) whichdefines the order of the hidden units according to the concentration ofthe energy. Here we assume that the original basis functions are notlinearly dependent.

The process is done in the following way. First, define S(m) as the setof indices of basis functions that have been chosen, through the m^(th)one.

${S(m)} = \left\{ \begin{matrix}\left\{ \phi \right\} & {{{for}\mspace{14mu} m} = 0} \\\left\{ {{j(1)},{j(2)},\ldots\mspace{14mu},{j(m)}} \right\} & {{{{for}\mspace{14mu} m} > 0},}\end{matrix} \right.$

Its complement S^(c)(m) is the set ofS ^(c)(m)={1,2,3, . . . ,N _(u) }−S(m)  (18)

where S^(c)(m−1) is the set of candidate BFs for the m^(th) iteration.At the m^(th) iteration there will be m−1 ordered BF that are defined bythe function values j(1) through j(m−1). During the execution of them^(th) iteration j(m) will take several values, the ones that comes fromS^(c)(m−1). At the end of the iteration, j(m) will take its value fromthe raw BF that keeps the most of the energy and S(m) is updatedaccording toS(m)=S(m−1)∪{j(m)}.  (19)

Because we are interested in finding the most important hidden unitsbasis functions, and are not interested in eliminating any inputs, thefirst N+1 basis functions are picked as,j(k)=k for 1≦k≦N+1,

Then for m=N+2, getting the first hidden BF since full connectivity isconsidered, the values of j(1) to j(N+1) correspond to the input unitsand threshold at the output layer and they are known. Here S(N+1) andS^(c)(N+1) are,S(m−1)=S(N+1)={1,2, . . . ,N,N+1}={j(1),j(2), . . . ,j(N+1)},

j(1) to j(N) correspond to the network inputs and j(N+1) corresponds tothe threshold. And the candidates BF are

$\begin{matrix}{{S^{c}\left( {N + 1} \right)} = {{S^{c}\left( {m - 1} \right)} = {\left\{ {1,2,3,\ldots\mspace{14mu},N_{u}} \right\} - {{S\left( {m - 1} \right)}.}}}} \\{{= {{S^{c}\left( {m - 1} \right)} = \left\{ {{N + 2},{N = 3},\ldots\mspace{14mu},N_{u}} \right\}}},}\end{matrix}$

where S^(c)(m−1) has N_(h) elements. For testing the candidate BF j(m)takes on all values in S^(c)(N+1) and after finding the BF that keepsthe most of the energy then j(m) takes its value and S(m) is updatedaccording to (19) asS(m)=S(N+2)=S(N+1)∪{j(N+2)}={j(1),j(2), . . . ,j(N+1),j(N+2)}.

For m=k the candidates BF are,S ^(c)(k−1)={1,2,3, . . . ,N _(u) }−{j(1),j(2), . . . ,j(k−1)},

with N_(u)−k+1 candidate BF. After testing all the candidate BF, j(k)takes its value andS(k)=S(k−1)∪{j(k)}={j(1),j(2), . . . ,j(k)}.

This is repeated until m=N_(u), and in this way the values of thefunction j(m) are found.

For doing the previous process it is necessary to estimate the energyfor the m^(th) candidate BF. This is done in the following way,

$\begin{matrix}{{\left. {P(m)} \right|_{{j{(m)}} \in {S^{c}{({m - 1})}}} = {\sum\limits_{i = 1}^{M}\left\lbrack {w_{o}^{\prime}\left( {i,m} \right)} \right\rbrack^{2}}},} & (20)\end{matrix}$

where the value of the energy is a function of the previous m−1 orderedBF and the BF that it is tested. In equation (20) P(m) is the energy ofthe m^(th) BF, where the m^(th) tested BF belongs to S^(c)(m−1). In thisway we are looking to concentrate the energy in the first BFs. Thendoing this and from equation (15) we obtain a method for doing pruningof the hidden units since the last columns of equation (15) (i.e. lastBFs) will contribute with the smallest amount in the summation, secondterm of equation (15), and then it is expected that eliminating theseBFs (hidden units) the error of the NN is not affected in a largeamount.

P(m) is obtained for all the candidates BF defined by (18). It should beobserved that for applying equation (20), obtaining coefficients a_(k1)from equation (17) is required. Then using these coefficients and thecrosscorrelation matrix in equation (14) the new w_(o)′(i,j) weights(columns of the output weight matrix) can be obtained. In this wayknowing a₀₀ the weights that correspond to the first column of theoutput weight matrix (energy of the first BF) can be obtained. In thesame way, knowing a₁₀ and a₁₁ the second column of w_(o)′(i,k) can becalculated, and so on.

The general idea and behavior of the Pseudogenetic Algorithm based uponthe standard Schmidt procedure is similar to the one used in GeneticAlgorithms (GAs), which is an optimization technique based in thesimulation of the natural law of the evolution of species by naturalselection, where only the fittest individual will be able to reproduce,handing down its chromosomes while the less fit will suffer extinction.Both work with a population of ANNs but in the proposed method theoperations over the population are different. The representation of thepopulation is not a string, but a set of weight matrices, but thebehavior of the new networks (sons) is similar to the original ones.From the functionality point of view there is some similitude betweenone of the proposed operations with the reproduction and crossoveroperation of the GAs' together. Because of this our method is called apseudogenetic algorithm.

In the proposed algorithm, once that the new ANN are created they areanalyzed by the modified Schmidt Procedure and then the best units ofthe new networks are selected.

Define the k^(th) input network N_(k) asN _(k) ={N,M,N _(h) ^(k) ,W ^(k) ,W _(O) ^(k) ,F}.

Here the superscript k defines the number of the network. N defines thenumber of inputs, M the number of outputs, N_(h) ^(k) is the number ofhidden units, W^(k) is the weight matrix of the first layer, and W_(o)^(k) is the output weight matrix of the k^(th) network. F is thetraining data file. The weight matrix of the first layer has dimensionN_(h) ^(k)×(N+1), while W_(o) ^(k) is a matrix of dimension M×(N+N_(h)^(k)+1).

In the proposed pseudogenetic algorithm there are two operations to beused on the population, which are defined in the following way. Thecombine operation generates a new network, which inherits in some degreethe behavior of the parents. Given two networks N_(k) and N_(i), thecombine operation is written as,N _(c)←Combine{N _(k) ,N _(i)},  (21)

the result of this operation is a network with the following definition,

${N_{c} = \left\{ {N,M,N_{h}^{c},W^{c},W_{o}^{c},F} \right\}},{{{where}\mspace{14mu} W^{c}} = \left\lbrack \frac{W^{k}}{W^{i}} \right\rbrack_{{({N_{k}^{i} + N_{h}^{k}})} \times {({N + 1})}}},{N_{h}^{c} = {N_{h}^{i} + {N_{h}^{k}.}}}$

Here the new combined network will have the same number of inputs andthe same number of outputs. The number of hidden units will be equal toN_(h) ^(i)+N_(h) ^(k). W^(c) is gotten adding more rows to the combinednetwork setting to zero the elements of these rows and then copying theright values to the new network.

The output weight matrix is obtained adding zeros (columns) to W_(o)^(k) then the weights are added that correspond to the hidden units ofW_(o) ^(i). Finally W_(o) ^(c) is found applying OWO to the combinednetwork.

The second operation is the pruning operation.N _(a)←Prune{N _(k) ,N _(hd)},  (22)

it performs the pruning of a given N_(k) network reducing the number ofhidden units to N_(hd), where N_(hd) is the desired number of hiddenunits. Here N_(k) has N_(hd) or more hidden units. The process is doneaccording to the procedure described in page 24 line 4 (to page 26 line20) where first the units of the output layer are ordered and then thefirst N_(hd) units (the best since it is expected that the most of theenergy is concentrated in this units) are kept.

Assume that the number of inputs, outputs, and hidden units is the samein the whole population. The general idea in the first algorithm is tocombine the input network N_(n) with the best previous network,obtaining a combined net with 2·N_(h) hidden units. Then this network ispruned to the original size of N_(h) hidden units.

The best network at iteration k is selected among the incoming network,the previous best network (selected at iteration k−1) and the prunednetwork (at iteration k). In the case of the first iteration (k=1), thefirst input network N₁ is also the best network.

The algorithm can be expressed in the following way:

1.—Generate λ neural networks (population), and define k=1. Then thepopulation={N₁, N₂, . . . , N_(λ)}.

2.—Input network N_(k). For k=1 go to step 5.

3.—Using expression 21 combine network N_(k) with the previous bestnetwork N_(B). Then N_(c)←Combine {N_(k), N_(B)}.

4.—Get the pruned network, using expression 22. Here N_(hd) is equal toN_(h), i.e. N_(a)←Prune {N_(c),N_(hd)}.

5.—Select the best network out of the; input (N_(k)), pruned (N_(a)),and the previous best one (N_(B)). For k=1 the pruned network is equalto N₁.

6.—Increment k, and if k is not greater than λ go to step 2.

By using the fast training block 41 a scheme for performing sensor datavalidation (shown in FIG. 4) is also included as part of the EmbeddedHealth Monitoring System. The fast training block 41 executes thealgorithm described from page 14 line 13 to page 15 line 17 fordesigning a sensor signal estimator (ISE 631). Also comparators 632-634,absolute value generators 636-638, and a FDI block 635 (ISE) are part ofthe sensor data validation scheme. The estimator (ISE 631) can beoptimized by using ONGFE's 40 pseudogenetic algorithm as described frompage 16 line 11 to page 29 line 14. Assuming a cluster with C_(x)correlated signals, which are extracted from the system 70, thevalidation process is conducted in the following way. After digitizationof the input analog sensor signals 61 the Data Acquisition block 62provides data to the Data Validation block 63. Referring to FIG. 4 C_(x)correlated signals (S₁, S₂, . . . , S_(cx)) are considered as input toISE estimator 631 in the form of a vector input (x_(p)) containing C_(x)elements (where p corresponds to the sampling number). The ISE 631generates an output vector y_(p) whose elements are the estimates (Ŝ₁,Ŝ₂, and Ŝ_(cx)) of the corresponding input signals. The elements of theoutput vector are used for comparing the estimated value with the actualsensor signal value. The first sensor signal estimate y_(p.1) (equal toŜ₁) is input to comparator 632. Also, to this comparator is fed theactual sensor signal value (S₁,). The output of the comparator 632 feedsthe absolute value generator 636. Then output of the absolute valuegenerator 636 defines the element |r_(p,1)| which is fed to the FDI ISE635. The process is repeated for each sensor signal in the cluster.Referring to FIG. 4 the second signal estimate y_(p.2) (equal to Ŝ₂)feeds comparator 633 as well as the actual sensor signal value (S₂).After the absolute value generator 637 a second element (|r_(p,2)|) isobtained and driven to the FDI ISE 635. The last signal estimateprovided by y_(p.cx) (equal to Ŝ_(Cx)) feeds the comparator 634. Thisestimate and the actual sensor signal value (S_(cx)) are used forgeneration of the last element. After the absolute value generator 638then |r_(p,cx)| feeds the FDI ISE 635. In this way a vector |r_(p)|,whose elements are the absolute residual values (|r_(p,1)|, |r_(p,2)|, .. . , |r_(p,cx)|) is processed by the FDI ISE 635 for determining thesensor data quality. According to the result of the sensor datavalidation process an output code is generated (SS_(cx)) to flag andidentify the sensor data condition. Sensor data, estimated values, andthe binary code are delivered in the output of the Data Validation block63. SS_(cx), is a code defined by C_(x)+1 bits (or elements in anarray). C_(x) bits are used for signaling the condition of the C_(x)sensors (a single bit per sensor). An additional bit is used forhandling the normal operation condition of the cluster. In addition tothe FDI ISE 635 the data validation block also compares the absolutevalue of each residual (|r_(p,1)|, |r_(p,2)| . . . , |r_(p,cx)|) valuewith a threshold value (S_(Th1), S_(Th2), . . . S_(Thcx)) for detectinga potential sensor failure. In this way when: |r_(p,1)|>S_(Th1) or|r_(p,2)|>S_(Th2) . . . or |r_(p,cx)|>S_(Thcx) then it is consideredthat a red line condition has been generated and then by identifyingwhich residual value is larger than the corresponding threshold thepotential faulty sensor is identified.

For performing the process addressed from page 29 line 15 to page 30line 23 key blocks are the estimator ISE 631 and the FDI ISE 635. Thedesign of the estimator ISE 631 and FDI ISE 635 involve the generationof a data training structure (that can also be defined in the form ofdata training file). In this way by using this data training structureand ONGFE both ISEs can be designed.

The data generation process for designing the estimator ISE 631 can bedefined as follows. An initial characterization process is carried outby conducting a sweeping process of the physical parameter that drivesthe sensor within the target operation range for normal sensoroperation. Take N_(v1) samples of the input sensor signal values withinthe operational range, where each sample defines the vectors x_(p)(where 1<p<N_(v1)). N_(v1) patterns can be defined according to thefollowing format with y_(p)=x_(p):

$\begin{matrix}{p_{p} = {\left\{ {x_{p},y_{p}} \right\} = \left\{ {\begin{bmatrix}x_{p,1} \\x_{p,2} \\\vdots \\x_{p,N}\end{bmatrix},\begin{bmatrix}y_{p,1} \\y_{p,2} \\\vdots \\y_{p,M}\end{bmatrix}} \right\}}} & (23)\end{matrix}$

The process can be defined by working with a single sensor in thecluster and considering two failure types (for example bias and noise).Seed the first sensor failure (for example in the case of bias by addinga voltage value in the sensor signal or adding an offset value to thedigitized signal). Take N_(v2) samples of the input sensor signal valueswithin the operational range, where each sample defines the vectorsx_(p) (where 1<p<N_(v2)). To each vector x_(p) include y_(p) to form apattern vector p_(p) according to expression 23. In this case y_(p)contains the expected sensor signals without failure. Seed the secondsensor failure (for example noise by adding a random signal to thedigitized sensor value). In a similar way as in the first seededfailure, obtain N_(v3) patterns. At the end a training data file withN_(v)=N_(v1)+N_(v2)+N_(v3) patterns are obtained and can be used fortraining the estimator ISE 631. Additional failures (from the lab ordetected on line) can be appended for training the estimator ISE 631.

In the case of the data generation for the FDI ISE 635 the process canbe defined (in a similar way as when working with the estimator ISE 631)by working with a single sensor in the cluster and considering twofailure types (for example bias and noise). After designing theestimator ISE 631, an initial characterization process is carried out byconducting a sweeping process of the physical parameter within thetarget operation range for a normal sensor operation. Record the N_(v1)readings. Generate a vector |r_(p)| for each reading (where|r_(p)|=|r_(p,1)|, |r_(p,2)| . . . , |r_(p,cx)|). Each vector |r_(p)|defines a vector with N elements, where N is the number of sensors inthe cluster (C_(x)) and p identifies the pattern number (where1≦p≦N_(v1)). Patterns can be defined according to the following format:

$\begin{matrix}{p_{p} = {\left\{ {x_{p},{Class\_ Id}} \right\} = {{\left\{ {\begin{bmatrix}x_{p,1} \\x_{p,2} \\\vdots \\x_{p,N}\end{bmatrix},{Class\_ Id}} \right\}\mspace{14mu}{with}\mspace{14mu} x_{p}} = {r_{p}}}}} & (24)\end{matrix}$

Where Class_Id is a number that identifies the sensor operatingcondition. For a sweep with healthy sensors set Class_Id equal to 1.Seed the first sensor failure (for example bias, by adding a voltagevalue in the sensor signal or adding an offset value to the digitizedsignal). Perform a second sweep and take N_(v2) samples of the inputsensor signal values within the operating range, where each sampledefines the vectors x_(p) (where 1<p<N_(v2)). For each vector x_(p)obtain the vector |r_(p)|. Add a Class_Id value (set to two) to formpatterns p_(p) (with subindex 1<p<N_(v2)), as defined in expression 24.Seed the second sensor failure (for example noise by adding a randomsignal to the digitized sensor value). In a similar way as in the firstseeded failure, obtain N_(v3) patterns and keeping the same Class_Id(equal to two). At the end a training data file with N_(v)=N_(v1)+N_(v2)N_(v3) patterns is obtained and can be used for training the estimatorISE 631. Additional failures (from the lab or detected on line) can beappended for training the estimator ISE 631.

To design the sensor signal estimator ISE 631 the training datastructure generation process described for the case of a single sensoraddressed from page 31 line 6 to page 32 line 2 can be repeated forcharacterization of additional sensors in the cluster.

To design the FDI ISE 635 the training data structure generation processdescribed for the case of a single sensor addressed from page 32 line 3to page 33 line 2 can be repeated for characterization of additionalsensors in the cluster. Class_id should be changed for working with then^(th) sensor, where for the n^(th) sensor Class_id=n+1. Combination ofsensor failures can be also considered, where each combination define anew Class_id.

To design the sensor signal estimator ISE 631 the training datastructure generation process described for the case of a single sensoraddressed from page 31 line 6 to page 32 line 2 can be repeated forcharacterization of additional failures in a single sensor within thecluster.

To design the FDI ISE 635 the training data structure generation processdescribed for the case of a single sensor addressed from page 32 line 3to page 33 line 2 can be repeated for characterization of additionalfailures in a single sensor within the cluster.

To design the sensor signal estimator ISE 631 the training datastructure generation process described for the case of a single sensoraddressed from page 31 line 6 to page 32 line 2 can be conducted on-lineby using the synchronization and communication mechanism 44 fortriggering training and feeding data associated with the new detectedcondition).

To design the FDI ISE 635 the training data structure generation processdescribed for the case of a single sensor addressed from page 32 line 3to page 33 line 2 can be conducted on-line by using the synchronizationand communication mechanism 44 for triggering training and feeding dataassociated with the new detected condition).

The scheme described from page 29 line 15 to page 34 line 2 for a singlecluster can be duplicated following the same process as many times asthe number of clusters (with correlated signals) in a single SS 60.

The features of the present invention are summarized as follows:

1. The ONGFE 40 is a computerized distributed health monitoring kernelbuilt upon advanced learning with characteristics that include: (a)designed for developing embedded applications; (b) fast learningalgorithm; (c) very high performance; (d) optimization by pseudogeneticalgorithm; (e) distributed processing; (f) synchronization andcommunication mechanisms; (g) scalable; (h) modular; and (e) expandable.

2. The ONGFE 40 has the capability of performing pattern recognition andfunction approximation. The ONGFE 40 embeds the desired capability intoISE which can be distributed among the Embedded Health MonitoringSystem. By performing pattern recognition ISE can conduct failure (a)detection and (b) identification, where a single function can beembedded in an ISE or both. By performing function approximation the ISEcan perform regression and in this way provide failure prognosticsassessments.

3. The ONGFE 40 provides ISE optimization by executing a pseudogeneticalgorithm.

4. The ONGFE 40 provides synchronization and communication capabilityfor interacting with secondary diagnostic modules 80, which can driveONGFE's internal blocks and functions. ONGFE provides health data andstatus that can drive SDM. In this way different diagnostics schemes canbe blended with ONGFE for implementing schemes where synergy andcollaborative behaviors can be created.

5. A scalar, modular, and very flexible hardware architecture provides adistributed computational platform for deploying and customizing theEmbedded Health Monitoring System. The system structure is depicted inFIG. 1.

6. The Embedded Health Monitoring System builds on Smart Sensors withvery low power consumption and standard hardware interfaces (wirelessand wired).

7. The EHMS based upon ONGFE provides a sensor data validation schemefor FDI in correlated sensors clusters.

8. The ONGFE provides a very flexible framework with fine systemgranularity (software and hardware) that enables tailoring FDI functionsamong components, subsystems, and system level.

9. The ONGFE provides a solid processing structure for real timeapplications because of its hierarchical and highly distributedarchitecture (software and hardware).

One skilled in the art will understand that the embodiment of thepresent invention as shown in the drawings and described above isexemplary only and not intended to be limiting.

It will thus be seen that the objects of the present invention have beenfully and effectively accomplished. It embodiments have been shown anddescribed for the purposes of illustrating the functional and structuralprinciples of the present invention and is subject to change withoutdeparture from such principles. Therefore, this invention includes allmodifications encompassed within the spirit and scope of the followingclaims.

What is claimed is:
 1. A system of health monitoring computer (HMC),adapted for communicating with a target system through a sensor networkand collecting health data from the target system, and for interactivelycommunicating with secondary diagnostic modules for the target system,comprising: an Embedded Health Monitoring based upon Optimized NeuroGenetic Fast Estimator (ONGFE), comprising a communication andsynchronization block interactively communicating with the secondarydiagnostic modules for the target system; a Health Monitoring InferenceMechanism (HMIM) communicating with said Optimized Neuro Genetic FastEstimator (ONGFE), having a plurality of Intelligent Software ElementsISEs which are designed and embedded in said Health Monitoring InferenceMechanism (HMIM) through said Optimized Neuro Genetic Fast Estimator(ONGFE), wherein said Health Monitoring Inference Mechanism (HMIM) isarranged for operatively communicating with the sensor network embeddedwith ISEs designed by said Optimized Neuro Genetic Fast Estimator(ONGFE), wherein said sensor network is arranged for extracting physicalparameters measurements from the target system and generating andinputting the health data including sensor data, status and features tosaid Health Monitoring Inference Mechanism (HMIM) and Embedded HealthMonitoring based upon Optimized Neuro Genetic Fast Estimator (ONGFE),wherein the sensor network comprises a plurality of smart sensors whichare customizable according to the target system, wherein a baselinesensor suit of the sensor network is formed with temperature, flow,pressure, and vibration sensors, wherein each of the smart sensorshaving low power consumption is capable of providing data acquisition,sensor data validation, a library of feature extraction algorithms andcommunication capabilities, wherein each of the smart sensors comprisesa sensor data validation core for signal processing; and a communicationblock communicating with said Health Monitoring Inference Mechanism(HMIM), wherein said Health Monitoring Inference Mechanism (HMIM)generates health assessments in response to the health data from thesensor network and provides the health assessments to said communicationblock for feeding Man Machine Interfaces of the target system; therebyeach of said Intelligent Software Elements ISEs, which are designedthrough said Optimized Neuro Genetic Fast Estimator (ONGFE) whichinteractively communicates with the secondary diagnostic modules for thetarget system and the sensor network, is capable of performing onefunction when the function is prognostic function, and is capable ofperforming one or more function when the function includes failuredetection function and failure identification function.
 2. The system,as recited in claim 1, wherein said communication block includes IEEE802.11.x, 100G Ethernet, and USB as core communication channels arrangedfor transferring data, including the health data, the health assessmentsand the data of failure prognostics functions, to Man Machine Interfaceother central or local computer.
 3. The system, as recited in claim 2,further comprising a Sensor Communication Block (SCB) having protocolsincluding Zigbee, IEEE 802.15.4, I²C, RS-232, and USB and comprisingcommunication channels interacting with the sensor network whichgenerates data packages which is capable of providing snapshots ofvibration signals in which time and sensor measurements are provided persample; measurement of temperature, pressure, and flow associated withtime and measurement magnitude; status information with data validation;identification number of the smart sensors; Channel number; and checksumvalue.
 4. The system, as recited in claim 3, wherein said ISE defines anArtificial Neural Network (ANN) which corresponds to an operand, whereinthe operand is a data structure which defines: number of inputs; numberof hidden units; number of outputs; input weight matrix; and outputweight matrix, thereby said ISEs are operands to a plurality of ONGFEfunctions which performs: instantiation, initialization, on-linetraining, network testing, network error calculation, processing inputvectors, pruning, combining networks, and ANN optimization bypseudogenetic algorithm.
 5. The system, as recited in claim 4, whereinsaid ONGFE further comprises a fast training block and a pseudogeneticblock, wherein said ONGFE designs and embeds fast learning algorithm tosaid health monitoring computer (HMC) for applying functions to saidISEs of said health monitoring inference mechanism (HMIM) for defininghigh performance ISEs, wherein said fast training block is capable ofperforming: on-line learning for updating and designing ISE datastructures of said ISEs; instantiation and training of said ISEs forperforming pattern recognition; instantiation and training of said ISEsfor performing function approximation; instantiation of a population ofsaid ISEs for defining P-ISEs; instantiation of said ISEs in said HMIM;and instantiation of said ISEs in said Smart Sensors, wherein saidPseudogenetic block of said ONGFE is arranged for evolving said ISEs foroptimization.
 6. The system, as recited in claim 5, wherein said ONGFEfurther comprises an optimization block that performs ISE optimizationby executing a preset pseudogenetic algorithm stored in saidoptimization block, wherein a preset population of said P-ISE is firstinstantiated by said fast training block, and then evolved through saidpseudogenetic block for conducting network optimization to provideresulting ISEs which can be embedded in said HMIM for enhancedprognostics and said Smart Sensors for enhanced sensor value estimation.7. The system, as recited in claim 6, wherein said fast training blockincludes a preset algorithm which is preformed through said fasttraining block for designing and defining a pattern recognition ISE forsaid resulting ISEs, such that said resulting ISEs can be embedded insaid HMIM for performing FDI at a component level which is defined ascomponent ISEs (ISE 31 and ISE 32), as well as at a system level byfusing the health data at component level which is defined as systemISEs (ISE 33), wherein said resulting ISEs can be embedded in said HMIMfor providing failure prognostic, which is defined as prognostic ISE(ISE 34), through said fast training block for function approximation todefine an output ISE which can be embedded in said Smart Sensor forperforming sensor data validation.
 8. The system, as recited in claim 7,wherein each said component ISEs (ISE 31 and ISE 32) is deployed for onepreset component in such a manner that said system is capable of beingexpanded through adding additional component ISEs.
 9. The system, asrecited in claim 8, wherein said system ISE (ISE 33) performs systemlevel FDI such that said HMIM can be reproduced following the samestructure for performing FDI in additional systems.
 10. The system, asrecited in claim 9, wherein said a synchronization block of said ONGFEis arranged for interaction with an external SDM and MMI such that theexternal SDM can trigger learning features of said ONGFE, wherein saidsynchronization block further defines two types of operations, which areinput synchronization operations and output synchronization operations,wherein said input synchronization operations includes: startingexecution of on-line training; reading SDM's health data package (rawsensor data, features, failure, and training data structure); andreading SDM status information, wherein said output synchronizationoperations includes: sending status information of said ONGFE; writinghealth data package of said ONGFE; and writing said status informationof said ONGFE.
 11. The system, as recited in claim 10, wherein said fasttraining block and said Synchronization block of said ONGFE enableimplementing evolving capability in the Health Monitoring System bytriggering a learning process when new conditions are recognized by saidONGFE.
 12. The system, as recited in claim 11, wherein said fasttraining block and said Synchronization block 44 of said ONGFE 40 enableimplementing diagnostics schemes in such a manner that said ONGFE caninteract in real time with said Secondary Diagnostic Modules and saidONGFE is capable of creating synergy and collaborative behaviors inresponse to said Secondary Diagnostic Modules.
 13. The system, asrecited in claim 12, wherein said Smart Sensor is a toolbox with a coreset of feature extraction algorithms embedded therein, wherein saidfeature extraction algorithms are; energy signal value (rms); kurtosis;crest factor; FFT; inverse FFT; and statistical indexes (such as mean,variance, and covariance).
 14. The system, as recited in claim 13,wherein said Smart Sensor embeds a method for conducting data validationin cluster of sensors (correlated sensors), wherein said methodcomprises the steps of: (a) performing design of sensor signalsestimator ISE 631 by using function estimation learning capability ofsaid ONGFE; (b) performing on-line sensor signals estimation by usingISE 631 of said ONGFE which has embedded function estimation capability;(c) generating a residual absolute value vector |r_(p)| where eachelement |r_(p,x)| is obtained by the absolute value of the difference ofS_(x)−Ŝ_(x); and (d) feeding said absolute values of each residualelement r_(p,x) obtained in step (14.c) from absolute value generatorsof said smart sensor to said ONGFE which has embedded FDI capability 635for performing sensor health assessment.
 15. The system, as recited inclaim 14, wherein said smart sensor further comprises a data validation63 block which includes a red line anomaly detection for FDI in thecluster sensor, where for each i^(th) sensor in the cluster, thecorresponding residual value (|r_(p,i)|) is compared with a thresholdvalue S_(Thi) such that when the absolute value of the residual value isbigger than the threshold value, a red line condition is defined andflagged.
 16. The system, as recited in claim 15, wherein said SmartSensor 60 is used for forming a network that provides a first level ofsaid system, wherein each said smart sensor 60 provides dataacquisition, data validation, feature extraction, and communicationcapability, wherein said Smart Sensor comprises a communication block 65which provides wireless communication (Zigbee) and wired networkingschemes (I²C, RS232, and SPI) in such a manner that the Smart Sensor iscapable of performing as wireless smart sensor and is capable ofconnecting through a common bus for implementing a wireless or wirednetwork.
 17. The system, as recited in claim 16, wherein said HMC 10collects sensor data and features from the Smart Sensor Network andfeeds the sensor data and features to said HMIM for conducting FDI&P,wherein said Communication Block 20 is capable of communication atsystem and subsystem level such that a plurality of said HMC 10 iscapable of being linked to the central computer which provides a secondlevel of networking.
 18. A method for conducting data validation incluster of sensors (correlated sensors) embedded in a smart sensor,which is adapted for communicating with a system of health monitoringcomputer (HMC) having a Optimized Neuro Genetic Fast Estimator ONGFE,comprising the steps of: (a) performing design of sensor signalsestimator ISE 631 by using function estimation learning capability ofthe ONGFE; (b) performing on-line sensor signals estimation by using theISE 631 of said ONGFE which has embedded function estimation capability;(c) generating a residual absolute value vector |r_(p)| where eachelement |r_(p,x)| is obtained by the absolute value of the difference ofS_(x)−Ŝ_(x); and (d) feeding said absolute values of each residualelement r_(p,x) obtained in step (18.c) from absolute value generatorsof said smart sensor to said ONGFE which has embedded FDI capability 635for performing sensor health assessment.
 19. The method, as recited inclaim 18, wherein in said step (a) further comprising the steps of:(a.1) sweeping physical parameter that drives the sensor output withinthe target operating range for normal sensor operation and record N_(v1)readings, wherein each of the readings defines a vector x_(p) (where1<p<N_(v1)) with C_(x) elements, where C_(x) is the number of sensors inthe cluster; (a.2) working with each said vector x_(p) to form a presetpattern as defined by expression (23) with y_(p)=x_(p); (a.3) addingsaid preset pattern in the step (a.2) to a training data file; (a.4)considering the first failure case, seeding the failure in the system,sweeping the physical parameter that drives the sensor output within thetarget operating range and record N_(v2) readings, wherein each of thereadings defines a vector x_(p) where 1<p<N_(v2); (a.5) working witheach of the vector x_(p) resulting from the sweeping process of the step(a.4) to form the preset pattern in which y_(p) is defined as a correctsensor output measurement that corresponds to a given physical parametervalue; (a.6) adding the resulting patterns for the first failure casefrom the step (a.5) to the training data file; (a.7) repeating the steps(a.4), (a.5), and (a.6) for every desired failure to be characterizedfor generating a resulting training data file; (a.8) using the resultingtraining data file from the step (a.7) to instantiate an ISE of saidONGFE and training the ISE by using a Fast training block 41 of theONGFE, wherein the fast training block 41 includes a preset algorithmwhich is preformed through said fast training block for designing anddefining a function approximation ISE for said ISE.
 20. The method, asrecited in claim 18, wherein the step (c) further comprises the stepsof: (c.1) performing data acquisition of sensor signals from the clusterby data acquisition block 62 of the smart sensor; (c.2) feeding thesensor signals to the estimator ISE 631 of the smart sensor forgeneration of sensor estimation values; (c.3) defining and feeding thefirst sensor estimated value Ŝ₁ into comparator 632 of the smart sensor;(c.4) obtaining and feeding actual sensor value S₁ into the comparator632 to generate the residual value r_(p,1); (c.5) feeding the residualvalue r_(p,1) into absolute value generator 636 of the smart sensor;(c.6) feeding |r_(p,1)| into FDI ISE 635 of the smart sensor; (c.7)repeating the steps (c.3), (c.4), (c.5) and (c.6) for each i^(th) sensorsignal, where 1≦i≦C_(x), being C_(x) the number of sensors in thecluster, that form the cluster and obtain the residual absolute value|r_(p,i)|; and (c.8) obtaining a vector r_(p) from the step (c.7) withelements defined by the residual absolute values |r_(p,i)|.
 21. Themethod, as recited in claim 18 wherein the step (d) further comprisesthe steps of: (d.1) sweeping the physical parameter that drives thesensor output within the target operating range for normal sensoroperation and record N_(v1) readings and generating a residual absolutevector for each reading, wherein each said residual absolute vectordefines a vector |r_(p)| with C_(x) elements, where C_(x) is the numberof sensors in the cluster and p identifies the pattern number (where1≦p≦N_(v1)); (d.2) working with each vector |r_(p)| to form a second setof preset pattern and setting a class id of the second set of presetpattern to 1; (d.3) adding the second set of preset patterns from thestep (d.2) to a second training data file; (d.4) considering the firstfailure case, seeding the first failure case into the system, sweepingphysical parameter that drives the sensor output within the targetoperating range and recording N_(v2) readings to generate a residualvector for each of the readings, wherein each of the readings defines avector |r_(p)| where 1<p<N_(v2); (d.5) working with each of the vectors|r_(p)| resulting from the sweeping process to form the second presetpattern, defining and setting the class Id to two; (d.6) adding thesecond set of preset pattern from the step (d.5) to the second trainingdata file; (d.7) repeating steps (d4), (d.5), and (d.6) for everydesired failure to be characterized, and keeping the classidentification number for the sequence of failure cases which areincluded in the second preset pattern; (d.8) repeating steps (d4),(d.5), (d6), and (d.7) for every desired failure to be characterized ina different sensor, and increasing the class identification number insequence according to the sensor number; and (d.9) using the resultingtraining data file to instantiate a ISE 635 and train the ISE 635 byusing ONGFE 40 of the system.
 22. The method, as recited in claim 21,wherein the ONGFE 40 comprises a synchronization and communicationmechanism 44 for triggering training and feeding data associated with adetected condition such that said ISE 631 is capable of performing thestep (d) in a remotely controlled manner through a wireless network.